초록

Digital media, such as images, audio, and video, can be readily manipulated, reproduced, and distributed over information networks. Therefore, a lot of research has been carried out to protect the copyright of digital media, and digital watermarking is one such copyright protection technique. Recently, 3D geometric models, such as 3D geometric CAD data, MPEG-4, and VRML, have been drawing a lot of attention, as such, various 3D watermarking algorithms have also been proposed to protect the copyright of 3D geometric data. Compared 3D geometric data to data of still image, audio, and video, it is very dissimilar to embed watermark in 3D geometric data because 3D graphic model has the different characteristics. That is, 3D graphic model in general is represented as the mesh that defined by the coordinate and the connectivity of vertices and it is easily modified by means of the geometrical or topological operation. And a model can be represented as various meshes consisted of the different vertices, edges and surfaces because there is not unique solution for representing 3D graphic model. The ordering of the data is also variable and not fixed. To increase the rendering speed in web 3D, the geometric data can be lessened by mesh simplification that remove the original mesh and generate the new mesh. Therefore, the above characteristics must be carefully considered for the mesh watermarking to have the robustness. Ohbuchi et al. proposed an algorithm that embeds a watermark in the mesh spectral domain based on the connectivity of mesh. Praun et al. proposed an algorithm that provides a scheme for constructing a set of scalar basis functions over the mesh vertices on the basis of the spread-spectrum principle. These algorithms have the robustness against the various geometrical and topological attacks, but if mesh connectivity altering of remeshing and mesh simplification happens, these algorithms require the resampling process of a suspect mesh for watermark extraction to obtain geometry of original mesh with a given connectivity information. Kanai et al. proposed a watermarking algorithm for 3D polygons using multiresolution wavelet decomposition. Yet, the application is restricted to a certain topological class of mesh, as the wavelet transform can only be applied to 4-to-1 subdivision connectivity schemes. Benedens also proposed an algorithm that embeds the watermark by modifying the distribution of mesh normal that included in the randomly selected bins of EGI, which is the factor that determines the shape of 3D object and is invariant to the topology deformation. Mesh normal distribution used by Benedens is very good at satisfying above requirement and expressing the shape characteristics of 3D mesh. But, if the partial geometric deformation such as cropping happens, the meshes included in these directional bins will disappear and also watermark embedded in those will be removed. Therefore, mesh watermarking is required not only to have robustness against remeshing, mesh simplification and cropping and but also to achieve the watermark extraction without the original mesh and the resampling process. We proposed the mesh watermarking that embeds the watermark into mesh normal direction based on the distribution of the complex weight magnitude of CEGI. The CEGI concept extends such a representation by adding the normal distance of the mesh to the origin as the phase component of the complex weight. It not only allows the pose of 3D mesh to be extracted, but also distinguishes a convex model from a nonconvex model having the same EGI representation.[56] Based on the characteristics of that, we can select effectively the watermark embedding location with the robustness against various attacks. Some cells for embedding the watermark are selected according to the rank of their magnitudes in each of patches after calculating the respective magnitude distributions of CEGI for 6 different patches of a mesh model. Each of the watermark bit is embedded into 6 cells with the same rank in these patch CEGI. Based on the patch center point and the rank table as watermark key, watermark extraction and realignment process are performed without the original mesh. The results of experiment verify that the proposed algorithm is imperceptible and robust against geometrical attacks of cropping, affine transformation and vertex randomization as well as topological attacks of remeshing and mesh simplification.